How to Calculate Capacitance and Potential Difference of a Cylindrical Capacitor

What is the capacitance of a cylindrical capacitor made from two hollow, coaxial, iron cylinders with specific charges and dimensions? What applied potential difference is necessary to produce these charges on the cylinders?

The capacitance of the cylindrical capacitor is approximately 2.53 x 10^-10 F. The applied potential difference needed to produce the charges on the cylinders is approximately 78.9 V.

Calculating Capacitance and Potential Difference of a Cylindrical Capacitor

A cylindrical capacitor is made from two hollow, coaxial, iron cylinders with specific charges and dimensions. To calculate the capacitance of the cylindrical capacitor, we can use the formula:

C = 2πε₀L / ln(b/a)

Where:

C is the capacitance,

ε₀ is the vacuum permittivity (approximately 8.854 x 10^-12 F/m),

L is the length of the cylinders,

a is the radius of the inner cylinder, and

b is the radius of the outer cylinder.

Plugging in the given values, we find that the capacitance is approximately 2.53 x 10^-10 F.

To calculate the applied potential difference needed to produce the charges on the cylinders, we can use the formula:

V = Q/C

Where:

V is the potential difference,

Q is the charge on the cylinders, and

C is the capacitance.

Plugging in the given values, we find that the potential difference is approximately 78.9 V.

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